3/4b+1/5b=37

Solution for 3/4b+1/5b=37 equation:

3/4b+1/5b=37

We move all terms to the left:

3/4b+1/5b-(37)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We calculate fractions


15b/20b^2+4b/20b^2-37=0

We multiply all the terms by the denominator


15b+4b-37*20b^2=0

We add all the numbers together, and all the variables

19b-37*20b^2=0

Wy multiply elements

-740b^2+19b=0

a = -740; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-740)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-740}=\frac{-38}{-1480}
=19/740
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-740}=\frac{0}{-1480}
=0
$